DOWNTOWN SAN DIEGO  The San Diego City Council voted unanimously Monday to extend through June 2015 its contract with Rural/Metro Corporation for ambulance service throughout the city.

The council also amended the contract to require an additional ambulance in the city’s relatively isolated South Bay neighborhoods, where emergency response times have been weak.

City officials said they still plan to open the ambulance contract up to other private sector companies in hopes of saving taxpayers money, but that such an agreement won’t be in place before Rural/Metro’s contract was due to expire on June 30.

The city is scheduled to open the contract for bids next month, with any transition to another provider expected to take at least 11 months. Rural/Metro has provided the city’s ambulance service since 1997.

The contract requires Rural/Metro to pay the city $10 million during the one-year extension. The company will cover that with revenue from ambulance rides, which will cost an average of $1,854, according to estimates included in the contract.

The additional South Bay ambulance, which is scheduled to begin service on Thursday and operate 12 hours per day, will cost $313,000. The city will cover $110,000 and Rural/Metro will cover $203,000.

Councilman David Alvarez, whose district includes the South Bay, said his constituents deserve another ambulance. “I’m glad we’re putting everyone in the city on a more equal playing field,” he said.